I am writing on behalf of my daughter Mel who is a sophomore in high
school. She is having a real problem with proofs. In particular two
column proofs. Can you explain the steps to prove geometric figures?

A line is 1 dimensional, a square or rectangle is 2 dimensional, and a
cube is 3 dimensional. My question is what if you throw in parabolas
or circles or the absolute value function, etc.? A circle is kind of
like a parabola, but it is very much like a square, so I am thinking
it is 2-dimensional. My conclusion is that the only 1 dimensional
object is a straight line, and a point is 0 dimensional, but I am not
confident that I am correct. Can you please clear this up for me?